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arXiv · 1712.02108

On the arithmetic Kakeya conjecture of Katz and Tao

Ben Green·Imre Ruzsa
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Abstract

The arithmetic Kakeya conjecture, formulated by Katz and Tao in 2002, is a statement about addition of finite sets. It is known to imply a form of the Kakeya conjecture, namely that the upper Minkowski dimension of a Besicovitch set in $\mathbb{R}^n$ is $n$. In this note we discuss this conjecture, giving a number of equivalent forms of it. We show that a natural finite field variant of it does hold. We also give some lower bounds.

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Ben Green, Imre Ruzsa. 2017-12-06. On the arithmetic Kakeya conjecture of Katz and Tao. https://arxiv.org/abs/1712.02108

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